A neutral density filter is an object the purpose of which is to attenuate incident radiation uniformly independent of wavelength, i.e. neutral with respect to wavelength. Because of its purpose, neutral density filters are often also called attenuators though not all attenuators are neutral. A neutral density filter is characterized by the percent of incident light transmitted or by its optical density (OD). If 10% of light is transmitted (T=0.1), the filter is said to be OD1. At T=0.01, the filter is OD 2 and at T=0.001 the filter is OD 3. EQU OD= -log T EQU with EQU T= I.sub.O /I.sub.T
wherein:
I.sub.O =incident light intensity, and PA1 I.sub.T =transmitted light intensity.
In any discussion of how electromagnetic waves interact with matter, one works with the solutions to Maxwell's equations in dense media. In these discussions various quantities are defined which simplify calculations and descriptions of the interactions. In optics the most commonly used quantity is the index of refraction and it is often a function of wavelength or frequency, temperature and direction.
Bulk absorbers make use of the physical properties of a bulk material or impurities suspended in a bulk material. In both cases, the attenuation of an incident electromagnetic wave can be characterized by an absorption coefficient which governs the exponential decay of the wave as it travels through the material. This coefficient is often derived in terms of a complex index of refraction which is itself a result of more fundamental properties.
In principle, colloidal suspensions, dyes, gels and other materials may qualify as bulk absorbers. However, the most common example of a bulk absorber in visible optics is a colored glass. Glass which normally transmits light with little attenuation is doped with impurities which absorb light through electronic transitions. Once absorbed, the light is re-radiated at longer wavelengths and/or coupled into the glass as heat.
To get a neutral density colored glass, one needs to add a variety of impurities in various concentrations so that the net effect is to develop an absorption coefficient which is uniform with respect to wavelength. Once a mixture is settled on, the density of the filter is modified by making the filter thicker or thinner. Unfortunately as the thickness is varied, the neutrality of the filter varies. Also good mixtures may not be found for certain target values of the absorption coefficient. This is the case with neutral density filters with optical densities of three or higher. The best neutral density colored glasses typically have optical densities equal to or less than one.
A plastic or synthetic material may be used instead of what is commonly referred to as glass. However, the expression "glass" is herein employed, as well as in the accompanying claims, to refer to organic and inorganic glass, plastics or synthetic materials for the volume absorber.
Bulk absorbers typically can handle high optical powers since any power absorbed (and hence heat generated) is distributed over a larger volume of material with typically larger thermal paths so that the optic stays cooler.
Colored glass absorbers also have generally low reflectance. This is useful when working with lasers since a direct reflection with high power can be very dangerous to a person or other pieces of equipment. However, they do not have a constant density over significant wavelengths. All these bulk absorbers are herein referred to as "volume absorbers."
Another class of attenuators are thin-film attenuators. These include multilayer dielectric attenuators and metal layer attenuators.
By making use of the properties of reflection one can through the use of stacks of quarter-wave dielectric layers construct mirrors with high reflectivity, and hence low transmission. Since a layer is a quarter-wave only at one wavelength, broadband dielectric attenuators consist of many stacks of quarter-wave layers of varying thicknesses.
Neutral density filters made from dielectric layers are intrinsically highly reflective. If energy is coupled directly into the layers as absorbed heat, the small thickness would heat so rapidly as to be destroyed since the heat would not be able to flow away from the layer faster than it was being absorbed. However since dielectrics tend to have very small absorption coefficients, multilayer dielectric mirrors are preferred for high power laser application.
The most common uses for multilayer dielectrics are as mirrors and as interference filters, i.e. filters which only let light of a particular wavelength through.
Metals reflect and absorb light due to the light induced movement of electrons within the metal. A metal layer has such a large absorption coefficient that only a very thin layer is needed. In the visible region many metals have varying indexes of refraction and so often designers of metal layer neutral density filters use a mixture of metals as an attenuator. Great success has been met at developing very neutral filters. The most common example is INCONEL, a mixture of three metals, and it is very neutral over wavelengths from 300 to 2000 nanometers. In principle, multiple metal layers may also have some application as neutral density filters, but INCONEL is itself so neutral and cheap as it is a single layer, that there is a question about the advantage of multiple metal layers as stand-alone neutral density filters.
Since metals absorb strongly, metal attenuators have not been useful for high powers, since the heat buildup is so rapid that the metal layer is destroyed. Metal absorbers are thus not volume absorbers.
As pointed out by H. A. Macleod, in Thin-Film Optical Filters (Macmillan Publishing Company, New York, second edition, 1986), p. 155, the overall density of two or more neutral density filters in series is simply the sum of the individual densities, provided that multiple reflections are not permitted to occur between the individual filters. However, this does not address the matter of low-volume absorbers of highly reflective material in series with bulk absorbers.
Reference may also be had to D. L. Franzen and L. B. Schmidt, Absolute Reference Calorimeter for Measuring High Power Laser Pulses, APPLIED OPTICS, Vol. 15, December 1976, pp. 3115 to 3117, and Laser Exposure Testing, MONTANA LASER OPTICS (1988), Table 4.3, Damage Profile for Output Reflectors, and Table 4.9 Damage Profile for Metal Mirrors.